WEBVTT
00:00:00.640 --> 00:00:07.920
Anthony scored two to the power of seven points in a board game and Noah scored seven to the power of two points.
00:00:08.560 --> 00:00:12.640
Determine who won the game and by how many points.
00:00:13.800 --> 00:00:23.200
So we’ve been given both Anthony and Noah’s scores expressed in terms of powers: two to the power of seven and seven to the power of two.
00:00:24.000 --> 00:00:30.160
In order to work out who won the game, we need to evaluate what each of these numbers are equal to.
00:00:31.080 --> 00:00:32.680
Let’s start with Anthony.
00:00:33.120 --> 00:00:45.760
Two to the power of seven means two multiplied by itself seven times: two multiplied by two multiplied by two multiplied by two multiplied by two multiplied by two multiplied by two.
00:00:46.720 --> 00:00:50.920
To evaluate this, we just keep doubling two.
00:00:51.800 --> 00:00:56.720
Two multiplied by two or two squared is four.
00:00:57.400 --> 00:01:02.440
Doubling this gives two cubed, which is eight.
00:01:03.280 --> 00:01:09.000
Doubling again gives two to the power of four, which is 16.
00:01:09.600 --> 00:01:15.280
Doubling 16 gives two to the power of five — 32.
00:01:15.960 --> 00:01:22.280
Doubling 32 gives two to the power of six, which is 64.
00:01:23.000 --> 00:01:30.240
Doubling one final time gives the value of two to the power of seven — 128.
00:01:31.040 --> 00:01:34.400
So we’ve worked out how many points Anthony scored.
00:01:34.880 --> 00:01:39.280
Two to the power of seven is equal to 128.
00:01:40.520 --> 00:01:43.800
Now, let’s consider how many points Noah scored.
00:01:44.280 --> 00:01:50.160
Seven to the power of two or seven squared is equal to seven multiplied by seven two times.
00:01:50.880 --> 00:01:52.720
This is equal to 49.
00:01:53.680 --> 00:01:58.560
So now, we know that Noah has scored 49 points.
00:01:59.480 --> 00:02:03.800
The person who won the game is the person who scored more points.
00:02:04.360 --> 00:02:06.920
So this person is Anthony.
00:02:07.680 --> 00:02:15.520
To work out by how many points Anthony won the game, we just need to subtract Noah’s score from Anthony’s.
00:02:16.160 --> 00:02:21.880
128 minus 49 is equal to 79.
00:02:22.680 --> 00:02:32.560
So evaluating both powers shows us that Antony won the game by 79 points.